Hi, andrew257!
Actually, the Signal to Noise ratio is in "db" u can write in two ways, such like that:
SNR (db) = 10 log Ps/Pn
where,
Ps = Signal Power
Pn = Noise Power
Since,
Ps = Vs²/Rs² and Pn= Vn²/Rn²
Let, Rs = Rn hence , we get
Ps/Pn = Vs²/Rs² ÷ Vn²/Rs² since Rs = Rn
Ps/Pn = Vs²/Vn²
OR
Ps/Pn = (Vs/Vn)²
Now,
SNR (db) = 10 log (Vs/Vn)²
SNR (db) = 20 log (Vs/Vn) Using Logrithmic Property
I hope u understand easily, this mathematically phenomenon.
Enjoy.............